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S4 Mathematics: Probability (Paper 3)
S4 Mathematics: Probability (Paper 3)
Ten original questions connect probability with counting and statistics: sixteen boys in forty gives 0.4, forty-six sixes in two hundred trials gives a relative frequency of 0.23, three hundred plays at 0.15 give 45 wins and five people line up in 120 ways. Conditional probabilities of one half and 0.6 follow, with ten thousand four-digit codes, fifteen pairs from six, an expected gain of two dollars, and the error that more trials must balance the count.
Direct answer For conditional probability replace the denominator with the given group, and separate permutations from combinations when counting.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S4 Mathematics: Probability |
| Level | Four basic, three advanced, two challenge and one error-repair item |
02 Questions (10 items)
- FoundationA class of 40 has 16 boys. One student is chosen at random. Find the probability of choosing a boy.
- FoundationA die is rolled 200 times and a six appears 46 times. Find the relative frequency of a six.
- FoundationA game wins with probability 0.15 each time. Find the expected number of wins in 300 plays.
- FoundationIn how many ways can 5 people stand in a line?
- IntermediateOf 30 students, 12 are girls and 6 of the girls wear glasses. Given that a girl is chosen, find the probability that she wears glasses.
- IntermediateA four-digit code is made from the digits 0 to 9 with repetition allowed. How many different codes are possible?
- IntermediateTwo representatives are chosen from 6 students, order not counted. How many selections are possible?
- ChallengeA raffle wins with probability 0.2 and pays 30 dollars, otherwise costs 5 dollars. Find the expected gain per play.
- ChallengeOf 50 people, 20 are men and 12 of the men like coffee. Given that a man is chosen, find the probability that he likes coffee.
- Error redoError repair: 100 tosses give 60 heads and a student says the next 100 must give exactly 50 heads. Is that right?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 0.4 (that is 2/5) | Sixteen out of forty gives 0.4. |
| 2 | 0.23 | Relative frequency is the count of successes divided by the number of trials. |
| 3 | 45 times | Expected count is three hundred times 0.15. |
| 4 | 120 ways | The choices fall from five to one, so multiply five down to one. |
| 5 | 1/2 | Given a girl, the denominator is the twelve girls and six of them wear glasses. |
| 6 | 10 000 codes | Each of the four positions has ten choices. |
| 7 | 15 selections | Six times five counts each pair twice, so divide by two. |
| 8 | 2 dollars | Multiply each outcome by its probability and add, giving six minus four. |
| 9 | 0.6 (that is 3/5) | Given a male, only the twenty men are in the denominator. |
| 10 | No | Relative frequency only approaches the theoretical value; independent trials do not correct themselves. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
